Optimal EPO dosing in hemodialysis patients using a non-linear model predictive control approach.

Anemia management with erythropoiesis stimulating agents is a challenging task in hemodialysis patients since their response to treatment varies highly. In general, it is difficult to achieve and maintain the predefined hemoglobin (Hgb) target levels in clinical practice. The aim of this study is to develop a fully personalizable controller scheme to stabilize Hgb levels within a narrow target window while keeping drug doses low to mitigate side effects. First in-silico results of this framework are presented in this paper. Based on a model of erythropoiesis we formulate a non-linear model predictive control (NMPC) algorithm for the individualized optimization of epoetin alfa (EPO) doses. Previous to this work, model parameters were estimated for individual patients using clinical data. The optimal control problem is formulated for a continuous drug administration. This is currently a hypothetical form of drug administration for EPO as it would require a programmable EPO pump similar to insulin pumps used to treat patients with diabetes mellitus. In each step of the NMPC method the open-loop problem is solved with a projected quasi-Newton method. The controller is successfully tested in-silico on several patient parameter sets. An appropriate control is feasible in the tested patients under the assumption that the controlled quantity is measured regularly and that continuous EPO administration is adjusted on a daily, weekly or monthly basis. Further, the controller satisfactorily handles the following challenging problems in simulations: bleedings, missed administrations and dosing errors.

Dynamical control of the dialysis process. Part II: An improved algorithm for the solution of a tracking problem.

An efficient algorithm for the optimization of process parameters during dialysis has been developed. By solving a tracking-problem for prescribed time courses of distinguished variables, it is possible to compute optimal concentrations of electrolytes in dialysate as well as an optimal rate of ultrafiltration. These variables are indirectly influencing the status of the patient and can be directly modelled. They are describing the important exchange processes between blood and dialysate as well as between the different distribution spaces within the patient during dialysis. Their time courses are determined by an individually identifiable patient model. The tracking problem was treated as a dynamic optimization problem, and a continuous descent procedure which is usually employed for solving unconstrained static optimization problems has been adapted in such a manner that it is applicable for the solution of this problem. The used method is characterized by its simple mode of application, short solution time and moderate storage need. Especially in cases of contradictional requirements for desired time courses of model outputs the used optimization method performs well.

Dynamical control of the dialysis process. Part I: Structural considerations and first mathematical approach.

Individual optimization of the dialysis process requires the (open-loop or closed-loop) control of many different variables, e.g. plasma ion concentrations, acid base state, volemic state and hemodynamic quantities. For this purpose a general concept for multiple-input-multiple-output (MIMO) control of the dialysis process is presented. The controlled variables have been differentiated into variables which can be modeled mechanistically (primary controlled variables, PCVs) and (hemodynamic) variables for which no mechanistic model has been developed up to now (secondary controlled variables, SCVs). Accordingly the controller is decomposed into two stages. Stage 1 contains an expert system which links the PCVs to the SCVs and provides the generation of optimal profiles for the PCVs with respect to maximum hemodynamic stability of the patient. Stage 2 is a tracking controller for the PCVs. An algorithm for the multidimensional tracking problem at stage 2 has been developed. It can be used for open-loop and future closed-loop control. The algorithm has been tested for 4 controlled (plasma Na+, plasma K+, plasma volume and ratio between intra- and extracellular volume) and 3 control variables (dialysate Na+, dialysate K+, ultrafiltration rate) up to now. It renders possible the exact tracking of the prescribed trajectories as long as all points are reachable under consideration of all physical and physiological boundary conditions. If they are not, appropriate weighting of the conflicting optimization goals must be applied. An extension towards more than 4 controlled variables is possible on principle. Main advantages of the method are its mathematical simplicity and the applicability of standard optimization subroutines.

A mathematical model for fundamental regulation processes in the cardiovascular system.

Based on the four compartment model by Grodins we develop a model for the response of the cardiovascular system to a short term submaximal workload. Basic mechanisms included in the model are Starling's law of the heart, the Bowditch effect and autoregulation in the peripheral regions. A fundamental assumption is that the action of the feedback control is represented by the baroceptor loop and minimizes a quadratic cost functional. Simulation results show that the model provides a satisfactory description of data obtained in bicycle ergometer tests.